Fig. 2: Topological structures of half bimerons and colloidal response.

a Schematic of the formation of half-Néel-bimeron. The bottom substrate is an alternating splay-bend distortion, and the top surface is along the x-axis. The half bimerons are produced in the bend regions (violet). b Micrographs of colloids in half bimerons. If the \(\hat{{{\bf{p}}}}\) orientation is φ = − 135°, the half bimeron is defined as the half-Néel-bimeron (1/2, 0, 0, − π/2). The black arrow points at the defect. The violet arrow represents \(\hat{{{\bf{p}}}}\). c If the \(\hat{{{\bf{p}}}}\) orientation is φ = 45°, the half bimeron is defined as the half-Néel-bimeron (1/2, 0, 0, π/2). d 3D half-Néel-bimeron (1/2, 0, 0, − π/2) string. e 3D half-Néel-bimeron (1/2, 0, 0, π/2) string. f Schematic vector field of the half-Néel-bimeron (1/2, 0, 0, − π/2); Red (blue) region shows that the y-component of the director is positive (negative), while the white region shows that the director is in-plane. g Different perspectives of the vector field wrapping the unit sphere. h Schematic vector field of half-Néel-bimeron (1/2, 0, 0, π/2). i Corresponding unit sphere. j Simulated topological profiles (blue frame from part (b)) of the two half-Néel-bimerons (1/2, 0, 0, − π/2) formed in the bend regions at x = L/2 and x = 5L/2. The color represents the component of the director field on the z-axis. k Topological structures (red frame from part (c)) of adjacent half-Néel-bimeron (1/2, 0, 0, π/2) at x = L/2 and half-Néel-bimeron (− 1/2, 0, 0, π/2) at x = 5L/2. l Experimental (Exp.) and simulated (Sim.) images of 3D mapping the half bimerons. The linearly polarized excitation lights for FCPM are marked in yellow. m Mapping of the interaction potential between colloid and half-Néel-bimeron (1/2, 0, 0, − π/2). The colloid with φ = − 135° has minimized potential at location 1 (black dashed line). n Potential mapping between colloid and half-Néel-bimeron (1/2, 0, 0, π/2). The colloid with φ = 45° is at location 2 (black dashed line). Red solid lines indicate the center of the skyrmion string (x = 0). (Scale bar, 20 μm).